Symbolic Computation: Poincare's inequality - geometric and analytic connections
Dr. Clemens PechsteinMay 10, 2011, noon AS 50
Poincare's inequality allows to estimate the L2 norm of a function over a domain by a constant factor times the L2 norm of its gradient, provided that the function has a vanishing mean value. The constant factor is related to the second eigenvalue of the Laplace operator on the domain and it is difficult to be determined.
In this talk, I will review results by Maz'ya and John which relate the Poincare constant to geometric quantities associtated to the domain. Also, I would like to present results by Rob Scheichl and myself that allow to estimate the Poincare constant of domains built from finite element meshes.